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MachineCalcs

True Position Calculator

GD&T true position from measured X and Y deviation, with maximum material condition (MMC) bonus tolerance and a pass/fail check. Metric and imperial.

Inputs

mm
mm
mm
mm
mm

Results

True position(⌖) ✓
0.2828 mm

Within tolerance.

Diameter of the tolerance zone the feature needs.

MMC bonus tolerance
0 mm

Allowed (tol + bonus)
0.3 mm

  • True position Ø = 2 × √(ΔX² + ΔY²): the deviation is a radius, so the zone is a diameter.
  • Pass when the true position diameter is within the allowed tolerance (position tolerance plus any MMC bonus).

How it works

True position reports how far a feature's axis is from where the drawing says it should be, as the diameter of the tolerance zone it actually needs: ⌖ = 2 · √(ΔX² + ΔY²) where ΔX and ΔY are the deviations of the measured axis from its basic (true) location. Because position tolerance is a cylindrical (diametral) zone, the radial deviation is doubled.

When the callout carries a maximum material condition (Ⓜ) modifier, the feature earns bonus tolerance as it departs from MMC. For a hole the bonus is actual − MMC; for a pin it is MMC − actual. The feature is acceptable when the true position diameter is within the position tolerance plus that bonus.

Worked example

A hole's axis is measured 0.1 mm off in X and 0.1 mm off in Y. The true position is 2 × √(0.1² + 0.1²) ≈ 0.283 mm — within a 0.3 mm position tolerance, so it passes at RFS. If the callout is at MMC with a 10.0 mm minimum hole that actually measures 10.2 mm, the bonus is 0.2 mm, so the allowed tolerance becomes 0.5 mm — a comfortable margin. The calculator shows exactly this.

Frequently asked questions

How do you calculate true position?
True position is the diameter of the smallest tolerance zone that contains the feature axis: Ø = 2 × √(ΔX² + ΔY²), where ΔX and ΔY are the measured deviations of the axis from its true (basic) location.
Why multiply by 2?
ΔX and ΔY give the radial distance of the axis from true position. The GD&T position tolerance is a diameter (a cylindrical zone), so the radius is doubled.
What is MMC bonus tolerance?
When the feature control frame carries an Ⓜ (maximum material condition) modifier, the position tolerance grows as the feature departs from MMC. The bonus equals that departure and is added to the stated position tolerance.
How is the bonus different for a hole versus a pin?
For a hole (internal feature) MMC is the smallest size, so bonus = actual − MMC (a bigger hole earns more). For a pin (external feature) MMC is the largest size, so bonus = MMC − actual (a smaller pin earns more).
How do I check pass or fail?
The feature passes when the true position diameter is less than or equal to the allowed tolerance — the stated position tolerance plus any MMC bonus.
What about three datums?
ΔX and ΔY are the in-plane deviations from the basic location, measured in the datum reference frame. Establish the part on its datums first; the deviations you enter are relative to the true position in that frame.

Method & assumptions

  • Two-dimensional (X-Y) position in a single datum reference frame; establish the part on its datums before measuring.
  • MMC bonus is the linear departure from the maximum-material size; LMC works the same way with the limits reversed.
  • For composite tolerances (PLTZF/FRTZF) the two tiers are checked separately — that's a dedicated calculation.

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